If you have the hardware on hand to start piecemeal swapping out pieces and testing viability, this would quickly surmount a solution for you, if you are stuck reverting/putting the part's together back in the old PC this process will be far slower.
Ram seems to work fine, 1 stick can obviously cause issues under the right circumstances so if you've already checked stick by stick - perhaps even go with a new set. Always worth swapping in a different hard drive and always worth checking each and every component piecemeal. Different PSU, Different GPU, Different Monitor, Different Ram, Different CPU, swapping out all of this with tested part's will of course point towards your motherboard being the actual culprit but that is a process.
And if you just so happen to in fact need a blind install of drivers, the process of swapping out part's piece by piece may prove fruitless. Typically only hardcore over clockers/enthusiast's would even need to do such a thing because they're the guys that will flash a system for peak performance even if it is strictly warranty prohibited, as example - realizing I had a gpu that could be flashed/turned into a better GPU as that skew simply had the hardware disabled on card I've flashed a ATI 9500 into a ATI 9700 - a generationally better gpu - tricky business and can cause the type of problem's you are dealing with, and can of course happen to a gpu on accident.
and if you removed the ability on your motherboard specifically, even harder to figure out and may still call for a blind install
One of these methods will surely work
Good Luck